# When a polynomial is divided by (x+2), the remainder is -19. When the same polynomial is divided by (x-1), the remainder is 2, how do you determine the remainder when the polynomial is divided by (x+2)(x-1)?

##### 3 Answers

#### Answer:

The remainder when dividing

#### Explanation:

Note that

Suppose

Then:

Hence [1]:

Hence [2]:

Subtract [2] from [1] to get

Then

So the remainder when dividing

#### Answer:

The remainder is

#### Explanation:

Call the polynomial

Because

Because

From these two facts we get:

So

and

Applying the Division Algorithm and the Remainder Theorem to

Subtitutuing in

# = (x+2)(x-1)Q_2(x) + 7(x+2) - 19#

# = (x+2)(x-1)Q_2(x) + 7x+ 14 - 19#

# = (x+2)(x-1)Q_2(x) + [7x - 5]#

The remainder is

#### Answer:

#### Explanation:

Let the **Poly.** in question be

We know that, the **Degree** of the **Remainder Poly. ** is **strictly**

**less** than that of the **Divisor Poly.**

So, when **Quadr. Poly.**

**Remainder Ploly.** must have a degree

Therefore, let us suppose that, the desired remainder is,

Symbolically, this can be said, as, let,

Now,

On the same lines,

Solving

remainder, **Respected JIM H. and George C.** have

readily obtained.

**Enjoy Maths.!**